Kim requested a second meeting with Trump in a letter this month, and Trump says, "we will be doing that".
The US started negotiations with South Korea previous year, following Mr Trump's criticism of the 2012 deal as a "one-way street".
He said the new trade agreement, which still needs approval by South Korea's parliament, was a sign of the strong partnership between the US and South Korea. He says USA automobiles, pharmaceuticals and agricultural products will gain better access to Korean markets.
"But given that many earlier incidents were seemingly provoked by human error, these measures are likely to save the lives of soldiers from both sides", he said.
Despite the Trump-Kim landmark summit in Singapore, there has been little concrete progress on denuclearization.
Mr Trump said the signing, which took place on the sidelines of the United Nation's General Assembly, was "a great day" for the US and South Korea.
No decision had yet been taken as to the venue, he said.
Trade analysts say changes to the South Korea agreement were largely cosmetic, as the president limited the scope of renegotiations by declining to invoke U.S. trade law that would have required congressional approval of the final deal.
Speaking at the United Nations, Trump says the relationship with the country whose leader he branded past year as "Little Rocket Man" is much improved.
Trump also says he's "excited" to be signing a new trade deal with South Korea.
The US secretary of state, Mike Pompeo, has been given the task of setting up a second summit and he told reporters in NY that he hoped to fly to Pyongyang soon.
If there is a through line to the still-evolving Trump doctrine on foreign policy, it is that the president will not subordinate American interests on the world stage, whether for economic, military or political gain.
"I'm confident that will happen", Pompeo replied to skepticism expressed by reporters at a news conference Monday alongside National Security Adviser John Bolton and U.S. Ambassador to the United Nations Nikki Haley.
The US president will speak to the General Assembly on Tuesday and will chair the Security Council for the first time on Wednesday. Moon is expected to convey to Trump a personal message from Kim delivered at their inter-Korean talks last week. But no American company sells much more than 10,000 cars a year in South Korea.
Kicking off his meetings, Trump addressed "the world drug problem and a big problem it is" at an event that saw 130 countries pledge in general terms to step up action to fight the illegal drug trade and combat addiction.
Trump has alternated between optimism and frustration since his historic June summit with Kim in Singapore, where the two sides announced plans to work toward a general goal of denuclearizing the Korean Peninsula.
As he begins the sequel to his stormy United Nations debut, U.S. President Donald Trump will again confront the dangers posed by North Korea's nuclear threat, though its shadow may appear somewhat less ominous than a year ago.
But the tone has warmed again since Kim met last week with South Korean President Moon Jae-in, who made his first visit to Pyongyang.
But holding onto Kavanaugh's nomination and going through an investigation is a political risk for Republicans . Meanwhile, Republicans viewed Ms Ford's requests as a way to delay voting on President Donald Trump's nominee.
Taylor is attending the NBA's Board of Governors meetings today in NY , which include owners and top basketball executives. Butler had requested a trade out of Minnesota even with training camp about to start on Tuesday, September 25.
CBS New York reports that the daycare was in a home and it was not yet clear if it was being run as a licensed care center. The ages of two children, a boy and a girl, remains unknown but police say the girl is in a serious condition.
A mock questioning of Brett Kavanaugh did not go so well, according to a report in the Washington Post . In response, Kelly tweeted that Feinstein had no way to know if Ford was a survivor of attempted rape .
This counteroffer reportedly requires Prof Ford to testify before Judge Kavanaugh, which goes against one of her conditions. Ford was later asked to submit prepared testimony and a biography before Friday if she plans to attend the hearing.
And in 2011 almost 200 people were killed when the MV Spice Islander I sank off Tanzania's Indian Ocean coast near Zanzibar. Red Cross volunteers engaged in rescue efforts on and around Ukara Island in Lake Victoria, Tanzania .
Knight's lawyers maintain he was acting in self-defence as he fled armed attackers when he ran over Mr Carter and Mr Sloan. TMZ reports Knight plead no contest to a charge of voluntary manslaughter, for which he will serve a total of 28 years.
Tropical Storm Kirk forms in the Atlantic
On Sept. 7, a tropical depression formed in the eastern Atlantic, about 500 miles west of the Cape Verde Islands. Tropical Storm Kirk has formed off the coast of Sierra Leone and will trek westward over the next week.
Several killed as gunmen attack military parade in Iran
In videos and pictures of the aftermath circulating on social media, rescue officials can be seen shifting injured to hospitals. Meanwhile, the Takfiri Daesh terrorist group claimed responsibility for the attack but provided no evidence for the claim.
Apple releases how-to videos for the Apple Watch Series 4
The iOS 12 .1 beta mainly includes the group FaceTime feature that was announced at WWDC but pulled from the iOS 12 betas. Long story short: One iPhone XS Max survived being in a bowl of fresh water for 30 minutes with no visible damage.
Over 54,000 still without power in Carolinas after Florence
Officials had anxious the water would overwhelm several pits where coal ash had been stored, potentially contaminating rivers. North Carolina governor Roy Cooper says the state is still tallying its storm damage, but says it will be in the billions .
China, Russia warn US of consequences over sanctions
All of them - defense related firms, officers of the GRU military intelligence agency, and people associated with the St. Beijing has not joined in the sanctions imposed on Moscow by the U.S. and its Western allies since 2014.
Mayfield leads Browns to 1st win since December 2016
After a winless streak lasting 635 days, the Browns staged a comeback Thursday night to beat New York Jets 21-17 in Cleveland . The rookie gunslinger led the Browns back from a 14-0 deficit, finishing the game completing 17-of-23 passes for 201 yards.
European Union trashes Theresa May's Brexit plan
On the subject of a second referendum vote, she said she would "not break up my country or disrespect the referendum result". Britain wants to controls its own immigration and make its own independent trade deals.
Jimmy Butler has Knicks, Nets on three-team trade list
He reportedly provided a list of one to three teams with which he would be open to signing a long-term deal, sources said . However, what they may be willing to part with given the 29-year-old is in the final year of his contract is unknown.